If $g(x) = ax+b$, where $a<0$ and g is defined from [1,3] to [0,2] then value of

Question

If $g(x) = ax+b$, where $a<0$ and g is defined from [1,3] to [0,2] then value of

$cot(cos^{-1}(|sinx|+|cosx|)+sin^{-1}(-|sinx|-|cosx|))$

I am not getting how to solve this can anyone help

options

• g(1)
• g(2)
• g(3)

Answer 1

range of $|sinx|+|cosx|$ is $[1,√2]$ and cos inverse and sin inverse can take input from [-1,1] implies that $|sinx|+|cosx|=1$ and in g(x) ,a<0 means it is decreasing function g(1)=2 and g(3)=0. Now value of cot(cos−1(|sinx|+|cosx|)+sin−1(−|sinx|−|cosx|)) comes 0 means g(3) is answer